Given an open domain (possibly unbounded) Omega aS,R (n) , we prove that uniformly elliptic second order differential operators, under nontangential boundary conditions, generate analytic semigroups in L (1)(Omega). We use a duality method, and, further, give estimates of first order derivatives for the resolvent and the semigroup, through properties of the generator in Sobolev spaces of negative order.
Parabolic equations in $L^1$ with general boundary conditions via duality methods
PARONETTO, FABIO
2010
Abstract
Given an open domain (possibly unbounded) Omega aS,R (n) , we prove that uniformly elliptic second order differential operators, under nontangential boundary conditions, generate analytic semigroups in L (1)(Omega). We use a duality method, and, further, give estimates of first order derivatives for the resolvent and the semigroup, through properties of the generator in Sobolev spaces of negative order.
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